This invention relates to non-linear type digital-to-analog converters effectively employable for obtaining pitch determining voltage signals in electronic musical instruments in which, for instance, voltage-controlled oscillators are employed as tone generators, and more particularly to a non-linear type digital-to-analog converter capable of producing an exponential function output having, as its exponent, a value corresponding to a digital input signal applied thereto.
In general, there are many cases in which the provision of an exponential function output having, as its exponent, a value corresponding to a digital input signal is required. For instance, in an electronic musical instrument employing a voltage-controlled oscillator as its tone generator it is necessary to control the voltage-controlled oscillator by the use of such an exponential function output as described above in order to obtain pitch determining voltage signals.
In order to meet this requirement, a digital-to-analog converter such as shown in FIG. 1. has been proposed. In this conventional digital-to-analog converter, a binary-coded input signal ranging from the least significant digit a.sub.o to the most significant digit a.sub.m-1 (which is keying information, for instance, m=6 in case of 61keys) is converted into an analog signal e.sub.o by a digital-to-analog conversion circuit D/A, and the analog signal thus obtained is introduced to a voltage-controlled oscillator through an exponential amplifier A. In this operation, the output e.sub.o is represented by e.sub.o = M.sub.1 (a.sub.o .times. 2.sup.o + a.sub.1 .times. 2.sup.1 - - - - + a.sub.m-1 .times. 2.sup.m-1), and the output E(out) of the amplifier A is represented by E(out) = M.sub.2 (M.sub.3 e.sub.o). In these equations, M.sub.1, M.sub.2 and M.sub.3 are the circuit constants, and each of a.sub.o, a.sub.1, . . . , a.sub.m-1 is either 0 or 1.
However, the conventional digital-to-analog converter is accompanied by the following difficulties:
1. Since the accuracy of the least significant bit in the conversion circuit 1 is .+-.50%, the conversion error of the converter is increased in the case when the number of bits is small, although the conversion accuracy thereof may be high in the case of full scale.
2. The exponential function characteristic of a transistor or a diode is, in general, utilized for the exponential operation of the exponential amplifier A, and therefore not only the operational accuracy but also the operational speed thereof cannot be as high as expected. This difficulty is due to the thermal characteristics of circuit elements such as those described above and to a noise signal of the order of 10.mu.V caused therein; that is, the difficulty is due to the fact that the operating characteristic of the amplifier, or the transistor or the diode is limited.